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On Bochner flat para-Kählerian manifolds

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Central European Journal of Mathematics

Abstract

Let B be the Bochner curvature tensor of a para-Kählerian manifold. It is proved that if the manifold is Bochner parallel (∇ B = 0), then it is Bochner flat (B = 0) or locally symmetric (∇ R = 0). Moreover, we define the notion of tha paraholomorphic pseudosymmetry of a para-Kählerian manifold. We find necessary and sufficient conditions for a Bochner flat para-Kählerian manifold to be paraholomorphically pseudosymmetric. Especially, in the case when the Ricci operator is diagonalizable, a Bochner flat para-Kählerian manifold is paraholomorphically pseudosymmetric if and only if the Ricci operator has at most two eigenvalues. A class of examples of manifolds of this kind is presented.

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Authors and Affiliations

  1. Institute of Mathematics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wroclaw, Poland

    Dorota Łuczyszyn

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  1. Dorota Łuczyszyn
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Łuczyszyn, D. On Bochner flat para-Kählerian manifolds. centr.eur.j.math. 3, 331–341 (2005). https://doi.org/10.2478/BF02499218

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  • DOI: https://doi.org/10.2478/BF02499218

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